Importance of a technology capable of measuring and evaluating properties such as optical properties, a shape of nano patterns, and the like, of nano samples in real time by a non-destructive manner or a non-contact manner during a manufacturing process, in industrial fields related to a semiconductor device, a flat panel display, nanobio, nanoimprint, thin film optics, and the like, which have been rapidly developed has been gradually increased. Therefore, in an ellipsometry used as measuring equipment for process in the industrial fields, the measuring precision and measuring accuracy have been gradually improved and the continuous improvement of a measuring speed for real-time measurement has been required.
A multichannel spectroscopic ellipsometer as shown in FIG. 1 among multichannel spectroscopic ellipsometers of the related art has been the most widely used. The multichannel spectroscopic ellipsometer has been well known as nano measuring equipment that uses a basic principle of measuring and analyzing a change in a polarization state of reflected light 300 or transmitted light by the sample 200 for a plurality of wavelengths when incident light 100 is incident to the sample 200 to find properties of the sample.
Describing core components of the multichannel spectroscopic ellipsometers of the related art, a light source 110, an achromatic aberration collimator 120 that changes light emitted from the light source 110 into parallel light, and a polarization modulation unit 125 that forms the parallel light into a specific polarization state are disposed on a line of the incident light 100 and a polarization analysis unit 305 that is an optical system for analyzing the polarization state of the reflected light, and an achromatic aberration optical focus system 330 that intensively irradiates the parallel light transmitting the polarizing analysis unit 305 on a local area is disposed on a line of the reflected light 300, wherein the intensively irradiated light transmits an optical fiber 340 or is directly incident to a slit of a multichannel spectrometer 350. The multichannel spectrometer includes a dispersion optical system 352 and a multichannel photometric detector 354 and the light transmitting the slit is dispersed by the dispersion optical system 352 to be irradiated on each pixel of the multichannel photometric detector 354 for each wavelength and a quantity of light incident to each pixel is measured as an electrical signal such as voltage or current.
Among various types of multichannel spectroscopic ellipsometers of the related art, a rotating-polarizer or analyzer spectroscopic ellipsometer and a rotating-compensator spectroscopic ellipsometer have been the most widely used, each of which uses a least-squares algorithm analysis method that measures Fourier coefficients or ellipsometric functions about a waveform of the intensity of light measured by the photometric detector when a linear polarizer or a compensator rotates at a predetermined speed by a multichannel photometric detector in real time and uses the measured values and a theoretical model for a sample to find properties of a sample.
A core component of the rotating-polarizer multichannel spectroscopic ellipsometers of the related art is configured of a linear polarizer in which the polarization modulation unit 125 rotates at constant velocity of FIG. 1, which is generally referred to as the polarizer. The polarization analysis unit 305 is configured of a linear polarizer that stops at any azimuth, which is generally referred to as an analyzer. Meanwhile, core components of the rotating-analyzer multichannel spectroscopic ellipsometer are the same as the components of the rotating-polarizer multichannel spectroscopic ellipsometer except that the polarizer, that is, the polarization modulation unit 125 is in a stop state and the analyzer instead rotates at constant velocity. Therefore, the rotating-polarizer (or analyzer) multichannel spectroscopic ellipsometers of the related art have the most ideal advantage in terms of spectroscopic measurement since the number of configured optical elements is relatively smallest and only the optical elements of achromatic aberration such as a prism linear polarizer are used. However, the rotating-polarizer multichannel spectroscopic ellipsometers of the related art have a critical disadvantage called residual polarization of the light source and the rotating-analyzer multichannel spectroscopic ellipsometers need to solve the polarization dependency problem of the photometric detector by calibration.
Meanwhile, the rotating-compensator multi-channel spectroscopic ellipsometers of the related art may be classified into a single rotating compensator and a double rotating compensator. First, the core structure of the single rotating-compensator multichannel spectroscopic ellipsometers is the same as the core structure of the rotating-polarizer multichannel spectroscopic ellipsometers of the related art except that the polarizer stops and the compensator rotating at constant velocity is added between the polarizer and the sample or between the sample and the analyzer.
Meanwhile, the core structure of the double rotating-compensator multichannel spectroscopic ellipsometers of the related art has the same structure of the single rotating-compensator multichannel spectroscopic ellipsometers of the related art except that one compensator is further added so that the compensators are each disposed at both sides of the sample, wherein these compensators each rotate at a uniform velocity ratio of an integer. Therefore, in the core structure of the rotating-compensator multichannel spectroscopic ellipsometers of the related art, the polarizer and the analyzer are in a stop state at the time of measurement. Therefore, the rotating-compensator multichannel spectroscopic ellipsometers of the related art does not have a problem of the polarization dependency problem of the light source and the photometric detector. However, for a broadband wavelength λ region, it is very difficult to manufacture the achromatic aberration compensator having a phase difference of λ/4. As a result, there are problems in terms of dispersion characteristics and equipment calibration of the compensator, complexity of a method for analyzing data, and the like.
Meanwhile, in order to obtain the Fourier coefficients or the ellipsometric functions for the waveform of the intensity of light, the rotating-element multichannel ellipsometers of the related art uses a fixed exposure measuring frequency per unit rotation and a fixed integration time of the multichannel photometric detector that is equal to an exposure measuring period. In order to measure the Fourier coefficients or the ellipsometric functions, the rotating-element multichannel ellipsometers of the related art adopts a method for measuring the exposure of a predetermined frequency M per unit measurement by each pixel of the multichannel photometric detector at a plurality of azimuths at equidistance for one turn period or a half of the turn period of the optical element while at least one optical element rotating at constant velocity. The rotating-polarizer or analyzer multichannel spectroscopic ellipsometers of the related art mainly use the case in which the exposure measuring frequency M per unit measurement is fixed to 4, the single rotating-compensator multichannel spectroscopic ellipsometers of the related art mainly use the case in which M is fixed to 8, and the double rotating-compensator multichannel spectroscopic ellipsometers of the related art mainly use the case in which M is fixed to 36.
Meanwhile, in the case of the rotating-element ellipsometers of the related art, since the difference in the intensity of light reflected or transmitted by the sample according to the material and structure of the sample is generally large, the integration time needs to increase so as to reduce the measuring error when the intensity of light to be measured is weak, but may be limited by the predetermined exposure measuring period.
To the contrary, when the measured intensity of light is excessively large, the photometric detector reaches a saturation state and therefore, the integration time needs to be reduced. In this case, as the integration time is smaller than the exposure measuring period, the standby time of the photometric detector is longer and longer, such that the measuring precision may be deteriorated.
When the intensity of light periodically changing over time t is measured in real time by using the integrating photometric detector, the rotating-element ellipsometer uses a method for analyzing a Fourier coefficient so as to analyze the waveform. Provided that there is no error in the measuring apparatus, the light intensity I(t) measured by the integrating photometric detector using electrical signal such as voltage or current for a specific wavelength may be represented by the following Equation.
                              I          ⁡                      (            t            )                          =                              I            dc                    ⁢                      {                          1              +                                                ∑                                      n                    =                    1                                    N                                ⁢                                  [                                                                                    α                                                  2                          ⁢                          n                                                                    ⁢                                              cos                        ⁡                                                  (                                                      4                            ⁢                            π                            ⁢                                                                                                                  ⁢                                                          nt                              /                              T                                                                                )                                                                                      +                                                                  β                                                  2                          ⁢                          n                                                                    ⁢                                              sin                        ⁡                                                  (                                                      4                            ⁢                            π                            ⁢                                                                                                                  ⁢                                                          nt                              /                              T                                                                                )                                                                                                      ]                                                      }                                              (        1        )            
In the above equation, Idc represents an average value of the intensity of light (or referred to as a 0-order Fourier coefficient), α2n and β2n represent normalized Fourier coefficients, and T represents a period. Here, 2N is not 0 but is a natural number that represents a highest order among the normalized Fourier coefficients.
Among various types of the rotating-element multichannel ellipsometers of the related art, in the case of the rotating-polarizer or rotating-analyzer multichannel ellipsometers of the related art, all the Fourier coefficients other than the normalized Fourier coefficients of a secondary term such as α2 and β2 in Equation (1) that is the intensity of light measured by the multichannel photometric detector have a value of 0 and therefore, N becomes 1.
In the case of the single rotating-compensator multichannel ellipsometers of the related art, only the Fourier coefficients of second and fourth-order terms such as α2, β2, α4, and β4 are not 0 and therefore, N becomes 2. Meanwhile, in the case of the double rotating-compensator ellipsometers of the related art, the Fourier coefficients of the effective highest order term in Equation (1) are α32 and β32 when two compensators rotate at constant velocity at a predetermined velocity ratio of 5:3 and therefore, N becomes 16.
In the multichannel ellipsometers, a method of more accurately obtaining the normalized Fourier coefficients α2n and β2n from the waveform of the intensity of light measured by the photometric detector as in the above Equation 1 is very important. The rotating-element multichannel ellipsometers of the related art that are the most widely spread have mainly used a CCD detector array, a photodiode detector array, and the like, as the multichannel photometric detector. The multichannel photometric detectors are referred to as the integrating photometric detector since the measured light quantity value is proportional to the intensity of light as well as integration time. The integrating photometric detector reduces or increases the integration time when the quantity of light is too large or insufficient at the time of measurement to perform the measurement under the appropriate conditions. However, the integration time needs to be equal or larger to or than the minimum integration time of the corresponding photometric detector at the time of measurement.
In order for the rotating-element multichannel ellipsometers of the related art to obtain the Fourier coefficients, the intensity of light periodically changing over time as in the equation (1) is measured by being divided M times per unit measurement at a predetermined time interval by the multichannel integrating photometric detector. In this case, the integration time accurately coincides with the divided time interval. For example, the exposure Sj measured under the conditions of, for example, Ti=T/M is represented by the following Equation (2).
                                                                                          S                  j                                =                                ⁢                                                      ∫                                                                  (                                                  j                          -                          1                                                )                                            ⁢                                              T                        /                        M                                                                                    jT                      /                      M                                                        ⁢                                                            I                      ⁡                                              (                        t                        )                                                              ⁢                                                                                  ⁢                                          ⅆ                      t                                                                                  ,                              (                                                      j                    =                    1                                    ,                  2                  ,                  3                  ,                  …                  ⁢                                                                          ,                  M                                )                                                                                        =                            ⁢                                                                                          I                                              d                        ⁢                                                                                                  ⁢                        c                                                              ⁢                    T                                    M                                +                                                      ∑                                          n                      =                      1                                        N                                    ⁢                                                                                                              I                                                      d                            ⁢                                                                                                                  ⁢                            c                                                                          ⁢                        T                                                                    2                        ⁢                                                                                                  ⁢                        n                        ⁢                                                                                                  ⁢                        π                                                              ⁢                                          sin                      ⁡                                              (                                                                              2                            ⁢                                                                                                                  ⁢                            n                            ⁢                                                                                                                  ⁢                            π                                                    M                                                )                                                                                                                                                                                  ⁢                              {                                                                            α                                              2                        ⁢                                                                                                  ⁢                        n                                                              ⁢                                          cos                      ⁡                                              [                                                                              2                            ⁢                                                                                                                  ⁢                            n                            ⁢                                                                                                                  ⁢                                                          π                              ⁡                                                              (                                                                                                      2                                    ⁢                                                                                                                                                  ⁢                                    j                                                                    -                                  1                                                                )                                                                                                              M                                                ]                                                                              +                                                            β                                              2                        ⁢                                                                                                  ⁢                        n                                                              ⁢                                          sin                      ⁡                                              [                                                                              2                            ⁢                                                                                                                  ⁢                            n                            ⁢                                                                                                                  ⁢                                                          π                              ⁡                                                              (                                                                                                      2                                    ⁢                                                                                                                                                  ⁢                                    j                                                                    -                                  1                                                                )                                                                                                              M                                                ]                                                                                            }                                                                        (        2        )            
When solving the normalized Fourier coefficient by a simultaneous equation like the above Equation (2), the Equation of the normalized Fourier coefficients α2n and β2n represented by the exposure Sj is obtained, which is referred to as Hadamard transform and has been used as a representative method of obtaining Fourier coefficients in the rotating-element multichannel ellipsometers of the related art. Therefore, only the multichannel integrating photometric detectors specially designed and manufactured to satisfy the conditions is used. However, the actual integrating photometric detectors read out the quantity of light accumulated in each pixel for the integration time and do not react with the incident light for the time initializing the state, that is, the readout time Tr. Therefore, the exposure of the above Equation (2) is corrected to the following Equation (3) in consideration of this situation.Sj=∫(j-1)T/M+TrT/MI(t)dt, (j=1,2,3, . . . , M)  (3)
In this case, under the assumption that the readout time Tr is very shorter than the measuring time interval T/M of exposure, an equation obtained by performing first-order approximation on Tr is used.
In the case of the rotating-polarizer or analyzer multichannel ellipsometers of the related art using the Hadmard transform, in the above Equation (1), T represents a mechanical turn period of the polarizer or the analyzer, N is 1 as described above, and the minimum value of the measuring frequency M of exposure measured for period T/2 is 3. However, β4 is additionally measured in order to see whether the system is in a normal state and thus, the measuring frequency of exposure is increased to 4. In this case, since the exposure values measured in each period have symmetry with respect to a period of T/2, four unknown coefficients Idc, α2, β2, and β4 can be measured from a simultaneous equation configured of only S1, S2, S3, and S4 measured at a first half period.
Meanwhile, in the case of the single rotating-compensator multichannel ellipsometers of the related art using the Hadamard transform, T represents the mechanical turn period of the compensator, N is 2, and the minimum value of the frequency M of exposure measured for period T/2 is 5. However, β8 is additionally measured so as to see whether the system is in a normal state and thus, the measuring frequency of exposure is increased to 8. In order to obtain six unknown coefficients Idc, α2, β2, α4, β4, and β8 from the measured value of Sj (j=1, 2, 3, . . . , 8) in consideration of the symmetry of the value of exposure measured like the previous case, the solution of simultaneous equation is used. In addition, in the case of the double rotating-compensator multichannel ellipsometers of the related art using the Hadamard transform, thirty six unknown coefficients are each obtained in a very complex form by solving thirty six simultaneous equations.
In the rotating-element multichannel ellipsometers of the related art, when the turn period of the optical element is T, the measured period is limited to T/2 or T and equations of different complex forms obtained by solving the simultaneous equation of Equation (2) for the measuring frequency M of exposure per unit measurement one by one are used. In addition, a method for correcting the readout time error by using the first-order approximation equation for the readout time for Equation (3) for the measured values Sj of exposure to obtain the average value Idc of the intensity of light and the normalized Fourier coefficients α2n and β2n is used. Therefore, the integration time of the photometric detector used in the rotating-element multichannel ellipsometers of the related art is fixed to T/M or has only a value smaller than T/M and as a result, it is impossible to increase the integration time by reducing the measuring frequency of exposure or changing the measuring period.
When using the Hadamard transform of the related art, a sum of the readout time and the integration time needs to be set to accurately coincide with the measuring time interval. Therefore, when the intensity of light is too strong, the quantity of light easily reaches the saturation state even for the short integration time and thus, a part of light beam needs to be blocked by additionally using the optical elements such as an iris diaphragm, a neutral density filter (ND filter), and the like, inevitably so as to reduce the output from the light source. To the contrary, when the intensity of light is weak, there is a need to increase the integration time, but an apparatus for the measuring period and the measuring frequency of exposure specially set according to a kind of the multichannel ellipsometers of the related art is configured and used and thus, the maximum value of the integration time may be limited to T/M.
A need exists for a development of new multichannel ellipsometers capable of solving the above problems.